Yet another spaceship thought experiment

Suppose there's a spaceship accelerating at a constant rate, say g, thanks to some magic rocket engine. This engine creates a constant force on the ship, which is sufficient to accelerate its constant mass at a constant rate. Supposing that the floor is perpendicular to the line of travel, the occupants will feel as though they are standing in Earth's surface.

To those occupants, the simulated feeling of gravity will continue indefinitely, even though to an observer at rest relative to their launchpad will perceive their acceleration to decrease as they approach the speed of light, correct? That's my intuitive sense of the situation, but I don't really understand why it would be true. Can someone explain further?

Suppose there's a spaceship accelerating at a constant rate, say g, thanks to some magic rocket engine. This engine creates a constant force on the ship, which is sufficient to accelerate its constant mass at a constant rate. Supposing that the floor is perpendicular to the line of travel, the occupants will feel as though they are standing in Earth's surface.

To those occupants, the simulated feeling of gravity will continue indefinitely, even though to an observer at rest relative to their launchpad will perceive their acceleration to decrease as they approach the speed of light, correct? That's my intuitive sense of the situation, but I don't really understand why it would be true. Can someone explain further?

For a conceptual picture, just think of approximating the constant acceleration by a lot of little instantanous micro-jump in velocity, with each velocity jump being by the same amount relative to the ship's current rest frame immediately before the jump, and the frequency of the jumps being constant according to the ship's clocks. But because of the velocity addition formula, this means that an observer in a fixed inertial frame will see each velocity jump as smaller and smaller in her own rest frame, and she'll also see the time between jumps increasing as the ship's clocks slow down in her frame.

How convenient, I was just looking for a physics forum to ask some questions about the Relativistic Rocket and came across this thread. :)

I am writing a science-fiction novel where an interstellar vessel of this type is employed. I have a BSc with Spec in Physics and have read the Usenet Relativistic Rocket article mentioned above in a previous post but I have some questions.

In my novel, I have a race that regularly travels to another solar system ~4 ly away. The following section from the "Relativistic Rocket" article gave me an idea.

>If you wish to pass by a distant star and return to Earth, but you don't need to
>stop there, then a looping route is better than a straight-out-and-back route. A
>good course is to head out at constant acceleration in a direction at about 45
>degrees to your destination. At the appropriate point you start a long arc such
>that the centrifugal acceleration you experience is also equivalent to earth
>gravity. After 3/4 of a circle you decelerate in a straight line until you arrive
>home.

This got me thinking about the best way to do regular travel between two stars. As the journey between the two stars would take several years, the ship carrying the travelers would have to be virtually self-sustaining and carry as much cargo and as many passengers as possible to make the trip worthwhile. This would imply the need for a relatively large ship. It would seem wise to set up a ferry system whereby one ship (the "Ferry") continues around a regular loop between the two stars. As the Ferry nears the star, a smaller shuttle leaves the Ferry to drop people off at the planet while a second shuttle brings people from the planet to the Ferry. This way only the smaller shuttles (and thereby passengers and supplies) need to be accelerated to and from a "stop" whereas the larger Ferry (and all equipment and systems necessary for the "long" trip) can make use of centrifugal acceleration as described above.

Now, if I understand the setup, as described in the article, a continuous loop between the two stars would simply be a giant circular path with a diameter equal to the distance between the two stars. The article says this "looping route is better" but better in what way? I assume it is better in terms of fuel usage but NOT travel time as the distance traversed is pi/2 times larger than a straight trip.

Now I have a few questions:
-What would be the time (and Proper Time) such a looping trip would take?
-If that time is significantly longer than a straight there-and-back trip could a compromise be made using an elliptical path instead of a circular one?
-Could the gravitational pull of the stars be used to improve the time or fuel requirements (or would the ship need to get too close to the stars for this to be practical?)
-If shuttles were used to pickup and dropoff passengers from the Ferry, how long would they need to be in transit? (Assume the shuttles can maintain accelerations larger than 1g to the extent and for the duration that a human could tolerate it.)
-Related to the above: Could one shuttle be used for pickup and dropoff, or would the shuttle picking people up from the planet have to leave before the dropoff shuttle arrives?

I am trying very hard to write a good science-fiction novel with extremely accurate science (especially physics as that is what I know best). Any assistance and suggestions anyone can give me would be very much appreciated.